Predicting Properties of Well Bore Treatment Fluids

ABSTRACT

Methods and systems for predicting properties of well bore treatment fluids are disclosed. An embodiment includes a method of predicting fluid properties comprising: determining an operational window for a well bore fluid system; collecting data at vertices of the operational window; and developing a model comprising predicted properties for a plurality of data points within the operational window, wherein developing the model uses Barycentric interpolation.

BACKGROUND

Well bore treatment fluids often are used in, e.g., well drilling,completion, and stimulation operations. Examples of such well boretreatment fluids include, but are not limited to, drilling fluids,cement compositions, spacer fluids, fracturing fluids, acidizing fluids,completion fluids, and the like. As used herein, the term “well boretreatment fluid” will be understood to mean any fluid that may be usedin a subterranean application in conjunction with a desired functionand/or for a desired purpose. The term “well bore treatment fluid” doesnot imply any particular action by the fluid. The well bore treatmentfluids may be introduced into a well bore in accordance with knowntechniques.

It may be desirable to know various properties of the well boretreatment fluids to accurately predict how the fluids should act uponbeing introduced into the well bore. Fluid properties that may beimportant when designing well bore treatment fluids include, but are notlimited to, rheological behavior, fluid loss, static gel strength,sedimentation, thickening time, compressive strength, viscosity, andfree water, among others. A particular fluid may be selected for use ina well bore based on one or more of these properties. For example, aspacer fluid may be selected having a rheology that maximizes thefluid's displacement efficiency. Additionally, optimizing a spacerfluid's rheology can also help to prevent fluid inversion due to fluiddensity differences between the fluids before and after the spacerfluid. By way of further example, a fracturing fluid may be selectedhaving a viscosity sufficient to generate fracture geometry andtransport proppant. The fluid design for a subterranean operation hastypically been based on both experience and laboratory testing, whereasthe use of modeling methods to predict fluid behavior has been limited.For example, fluid design can require extensive laboratory time to testa number of different fluid formulations before a well bore treatmentfluid having desirable properties may be selected.

BRIEF DESCRIPTION OF THE DRAWINGS

These drawings illustrate certain aspects of some of the embodiments ofthe present invention, and should not be used to limit or define theinvention.

FIG. 1 is a flow chart illustrating an example method for predictingproperties of well bore treatment fluids.

FIG. 2 is a flow chart illustrating an example method for predictingrheological properties of well bore treatment fluids.

FIG. 3 is an example computer system that may be used in embodiments ofthe present techniques.

FIG. 4 is an example operational window that may be used in examplemethods for predicting rheological properties.

FIG. 5 is another example of an operational window that may be used inexample methods for predicting rheological properties.

FIG. 6 is a particle suspension chart that may be used in determining anoperational window in embodiments of the present techniques.

DESCRIPTION OF PREFERRED EMBODIMENTS

Embodiments of the present techniques relate to predicting properties,such as rheological properties, of well bore treatment fluids. Inaccordance with present embodiments, the properties may be predictedwith a limited amount of lab testing. Accordingly, costs may be savedand a competitive advantage may be gained by reducing the amount of labtime that may be required to design a fluid for use in subterraneanoperations. Among other things, embodiments may allow the design of afluid with minimal customer notice, thus giving the opportunity forreduced rig time, improved bond logs, and/or better customersatisfaction.

Embodiments disclosed herein related to design of a well bore treatmentfluid for use in subterranean operations. Subterranean operations inwhich the well bore treatment fluids may be used include well drilling,completion, and stimulation operations. Examples of such well boretreatment fluids include, but are not limited to, drilling fluids,cement compositions, spacer fluids, fracturing fluids, acidizing fluids,completion fluids, and the like. In some embodiments, methods may employBarycentric interpolation to develop a model that includes predictedproperties such as rheological data for a plurality of data pointswithin the boundaries of a fluid system. A well bore treatment fluid maythen be designed using the model. One example of such a well boretreatment fluid is a spacer fluid. Embodiments may be particularlyadvantageous for spacer fluids due to the fluid rheologies that aretypically required when using these fluids. In particular, optimizedrheology may be important for spacer fluids, for example, to ensureproper hole cleaning, fluid separation, and efficient fluid recovery anddisplacement.

An embodiment provides a method of predicting fluid propertiescomprising: determining an operational window for a well bore fluidsystem; collecting data at vertices of the operational window; anddeveloping a model comprising predicted properties for a plurality ofdata points within the operational window, wherein developing the modeluses Barycentric interpolation.

Another embodiment provides a method of servicing a well borecomprising: providing an optimized treatment fluid, wherein theoptimized treatment fluid is based, at least in part, on a modeldeveloped using Barycentric interpolation; and introducing the treatmentfluid into a well bore.

Yet another embodiment provides a fluid property prediction systemcomprising: memory; and a processor coupled to the memory, wherein theprocessor is configured to receive data for a fluid system and develop amodel using Barycentric interpolation, the model comprising predictedproperties for a plurality of data points within an operational windowof the fluid system.

FIG. 1 is a flow chart illustrating an example method for predictingproperties of well bore treatment fluids. As shown in step 2, the methodmay include determining an operational window for a fluid system. Themethod may further include collecting data at vertices of theoperational window (step 4). Once the data is collected, a model may bedeveloped (step 6) that includes predicted properties (such asrheological data) for a plurality of data points within the operationalwindow of the fluid system, wherein Barycentric interpolation is used indeveloping the model.

The operational window generally may define the boundaries of the fluidsystem. Two or more boundary conditions may be used to determine theoperational window. Non-limiting examples of boundary conditions thatmay be used in developing the operational window include, withoutlimitation, rheology, compressive strength, fluid loss, static gelstrength, sedimentation, thickening time, free water, cement mechanicalproperties (e.g., Young's modulus, Poisson's ratio, specific heat,thermal conductivity, and post-set expansion), wettability, emulsion,break time, pH, post-set permeability, hydration time, post-setporosity, mass or volumetric ratio of an additive (e.g., weightingadditive, viscosifier, fluid loss control additive, proppant, etc) towater, additive concentration (e.g., cement set retarder, fluid losscontrol additive, proppant, crosslinking agent, friction reducer,buffer, surfactant), density, viscosity, temperature, foam quality,permeability, expansion, water properties (e.g., pH, chlorides,bicarbonates, iron, tannin/lignins, carbonates, sulfates, magnesium, andcalcium concentration), fluid break time (e.g., for fracturing fluids),and proppant size. In one particular embodiment, the boundary conditionsmay be ratio of weighting additive to water and ratio of viscosifier towater. In another particular embodiment, the boundary conditions may betemperature and thickening time or free water. Two boundary conditionsmay be defined for a two-dimensional operational window. For athree-dimensional operational window, three boundary conditions may bedefined. In some embodiments, multiple operation windows may be definedand the interpolation may occur across dimensions.

Three or more points or vertices may be selected that define theoperational window. By way of example, a two-dimensional operationalwindow may be defined as follows: Vertex 1 (x₂, y₁), Vertex 2 (x₂, y₂),. . . Vertex n (x_(n), y_(n)), wherein n is the number of verticesdefining the operational window, x is a first boundary condition, and yis a second boundary condition. In some embodiments, the operationalwindow may be a triangular window that is defined by three vertices.FIG. 4 is a graphical representation of an example triangularoperational window. FIG. 4 will be described in more detail below. Infurther embodiments, the boundary conditions at each vertex may be massratio of weighting additive to water and mass ratio of viscosifier towater. By way of further example, a three-dimensional operational windowmay be defined as follows: Vertex 1 (x₁, y₁, z₁), Vertex 2 (x₂, y₂, z₂),and Vertex n (x_(n), y_(n), z_(n)), wherein n is the number of verticesdefining the operational window, x is a first boundary condition, y is asecond boundary condition, and z is a third boundary condition.

In some embodiments, the operational window may be determined based onthe functional boundaries of the fluid system. By way of example, themaximum and/or minimum of each boundary condition may be used to defineone or more vertices of the operational window. The functionalboundaries of a fluid system may be generally defined by the operationallimits of a fluid, for example, the limits of the particular boundaryconditions for the fluid system. In one embodiment, Vertex 1 may bedefined as the maximum viscosifier, Vertex 2 may be defined as themaximum weighting additive, and Vertex 3 may be defined as the minimumviscosifier and minimum weighting/no weighting additive. By way ofexample, a three-dimensional operational window may be defined asfollows, wherein the x-axis is weight ratio of weighting additive andthe y-axis is weight ratio of viscosifier to water: Vertex 1 (0, y₁),Vertex 2 (x₂, y₂), Vertex 3 (0, y₃), wherein y₁ is the maximum weightratio of viscosifier to water, x₂ is the maximum weight ratio ofweighting additive to viscosifier, y₂ is the minimum weight ratio ofviscosifier to water, and y₃ is the minimum weight ratio of viscosifierto water. Those of ordinary skill in the art, with the benefit of thisdisclosure, should be able to deteimine functional boundaries of a fluidsystem, for example, using lab testing or other appropriatemethodologies.

In some embodiments, the operational window may be divided into two ormore sub-windows, for example, to increase the accuracy of the propertyprediction. By way of example, one or more points may be selected onedges of the operational windows that could be used to divide theoperational window into sub-windows. In particular embodiments, theoperational window may be divided into two, three, four, five, six, ormore sub-windows. FIG. 5 is a graphical illustration of an exampleoperational window that has been divided into four sub-windows. FIG. 5will be described in more detail below. By dividing the operationalwindow in this manner, the interpolation technique may be refined toincrease the accuracy of the resultant property prediction.

As illustrated, the example method at step 4 may include collecting dataat vertices of the operational window. In particular embodiments, thecollecting the data may include collecting data at vertices of eachsub-window that has been created, for example, by division of theoperational window. The collected data generally may be related todesirable properties of the fluid system relative to subterraneanoperations. By way of example, the collected data related to one or moreof the following properties: rheology, compressive strength, fluid loss,static gel strength, sedimentation, thickening time, free water, cementmechanical properties (e.g., Young's modulus, Poisson's ratio, specificheat, thermal conductivity, and post-set expansion), wettability,emulsion, break time, pH, post-set permeability, hydration time,post-set porosity. Data may be collected using standard laboratorytechniques or other suitable methodologies. In some embodiments,historical data may be used so that additional laboratory testing maynot be required.

At step 6, the example method may further include developing a modelthat includes predicted properties (such as rheological data) for aplurality of data points within the operational window of the fluidsystem. Each data point may correspond to a fluid having a specificcomposition, wherein the model predicts properties for the particularfluid represented by that data point. Density may be also determined foreach of the data points within the operational window. In someembodiments, methods may employ Barycentric interpolation to develop themodel within the operational window. By way of example, Barycentricinterpolation may be used to interpolate one or more properties for aplurality data points within the operational window. Embodiments may useMicrosoft Excel or other suitable software program may be used toimplement disclosed interpolation techniques using a processor, forexample. The Barycentric interpolation may use the collected data forthe vertices of the operational window (or sub-windows) as the knowndata points in the interpolation. The interpolation technique may beadjusted to generate any number of data points within operationalwindow. By way of example, the interpolation technique may generate atleast 100, at least 1,000, or at least 10,000 data points within theoperational window. In additional embodiments, a specific set of resultsmay be determined by determining a specific data point based on enteredboundary conditions. By way of example, two or more boundary conditionsmay be entered and the model may predict properties at those particularboundary conditions.

Once a model has been developed using Barycentric interpolation, forexample, the model may be used in selection of a well bore treatmentfluid for use in a subterranean operation. By way of example, a wellbore treatment fluid may be selected for use in a subterranean operationbased on the model. As the model should contain a number of differentdata points (e.g., density, predicted properties, etc.) for the fluidsystem, the data points generally represent a set of potential fluids. Auser may select a fluid from this set of potential fluids havingdesirable properties. In some embodiments, the method may includeinputting desirable properties wherein the method compares the inputtedproperties to the predicted properties model to determine one or morepotential fluids having optimum properties. By way of example, inresponse to the comparison, one or more data points (which correspond topotential fluids, for example) may be output. In particular embodimentsfor spacer fluids, rheology data for the fluid (e.g., a drilling fluid)ahead of the spacer fluid and the fluid (e.g., a cement composition)behind the spacer fluid may be compared to the model to determine one ormore potential fluids having optimum properties. In further embodiments,additional properties may be input including, for example, desireddensity of the fluid, anticipated pump rates, and well geometry. Oncethe fluid or a set of fluids has been selected, the selected fluid maybe further refined, for example, by use of simulation and/or laboratorytesting.

In some embodiments, the model may be used to predict properties withinthe operational window based off a change in density by changing theconcentration of water in the fluid system. This may be desirable, forexample, to allow for onsite adjustments to a particular well bore fluidat the well site. In particular embodiments, water concentration may bechanged at the well site to change the rheology of the fluid.

FIG. 2 is a flow chart illustrating another example method forpredicting properties of well bore treatment fluids. The embodimentillustrated on FIG. 2 relates to prediction of properties for a wellbore spacer system. As illustrated on FIG. 2, the method at step 8 mayinclude determining an operational window for a well bore spacer system.The method may further include dividing the operational window intosub-windows at step 10. Rheology data may then be collected at verticesof the sub-windows (step 12). Once the data is collected, a model may bedeveloped, as shown at step 14, that includes predicted rheological datafor a plurality of data points within the operational window of thefluid system, wherein Barycentric interpolation is used in developingthe model.

In some embodiments, one or more parameters of the well bore spacersystem may be pre-defined. In some embodiments, the components of thewell bore spacer system may also be pre-defined. By way of example,present embodiments may be used to predict properties of a well borespacer system having pre-defined components. In some embodiments,relative proportions of certain components may also be pre-defined.Properties may be predicted using a well bore spacer system thatcomprises, for example, an aqueous component, a weighting additive, anda viscosifier. The well bore spacer system may also comprise one or moreof a dispersant, lost circulation material, surfactant, buffer, claycontrol additive, salt, thixotropic additive, and dye, among others.Heavyweight additives may be included in a spacer fluid to increase thedensity of the spacer fluid while still maintaining the necessary fluidproperties (e.g., fluid rheologies). A spacer fluid having an increaseddensity may be desirable to more precisely match the densities of thedrilling fluid and/or cement composition in the well bore. Examples ofheavyweight additives that may be used include, but are not limited to,hematite, hausmannite, barite, cement kiln dust, and sand. Theviscosifier may be included in the spacer fluid system, for example, toaid in the control of free water and/or for solids suspension. Examplesof viscosifiers that may be used include, but are not limited to, guargums, xanthan gums, diutan gums, carboxymethyl-hydroxyethyl cellulose,and clays (e.g., bentonite, etc.).

As previously mentioned, the operational window generally may define theboundaries of a fluid system. In the illustrated embodiment, theoperational window generally may define the boundaries of the well borespacer system. The operational window may be defined as previouslydescribed in accordance with FIG. 1. By way of example, two or moreboundary conditions may be used in defining the operational window ofthe spacer fluid system. In some embodiments, a two-dimensionaltriangular operational window may be defined. The boundary conditionsused in defining the operational window may comprise, for example,weight ratio of weighting additive to water (“HWR”) and weight ratio ofviscosifier to water (“VWR”). Accordingly, a two-dimensional operationalwindow may be defined as follows: Vertex 1 (x₁, y₁), Vertex 2 (x₂, y₂),and Vertex 3 (x₃, y₃), wherein x is HWR and y VWR.

In accordance with present embodiments, the functional boundaries of thespacer fluid system may be used to define the operational window. By wayof example, functional boundaries may include maximum VWR, minimum VWR,and maximum HWR. The maximum VWR may be the VWR above which the fluidsystem is unmixable. In one embodiment, the maximum VWR may bedetermined by maximizing the VWR until an unmixable concentration of theviscosity and water is achieved. The maximum VWR may be determined witha HWR of 0. Another functional boundary may include the minimum HWR.Minimum VWR may be the VWR below which solids cannot be suspended. Inone embodiment, the minimum VWR may be determined by calculating theminimum amount of viscosifier required to suspend the heavyweightadditive at low shear rate. Yet another functional boundary may includemaximum HWR, which may be determined at minimum VWR. In one embodiment,maximum HWR may be determined by maximizing the HWR until an unmixableconcentration of heavyweight additive in water (at minimum VWR) isachieved. FIG. 4 is a graphical representation of an example triangularoperational window having three vertices defined by HWR and VWR. Vertex1 is the maximum VWR, Vertex 2 is the minimum VWR at maximum HWR, andVertex 3 is the minimum HWR at minimum VWR.

At step 10, the operational window may be divided into two or moresub-windows. This sub-division should increase the accuracy of theproperty prediction. By way of example, one or more points may beselected on edges of the operational windows that could be used todivide the operational window into sub-windows. For example, one pointedselected on the edge connecting Vertex 1 and Vertex 2, for example, onthe midpoint of the edge. Another point may be selected on the edgeconnecting Vertex 2 and Vertex 3, for example, on the midpoint of theedge. Yet another point may be selected on the edge connecting Vertex 1and 3, for example, on the midpoint of the edge. These three additionalpoints may be used to divide the operational window into foursub-windows, as illustrated in FIG. 5.

At step 12, the example method may include collecting rheology data atthe vertices of the sub-windows. Additional data may be collectedrelated to one or more of the following properties: rheology,compressive strength, fluid loss, static gel strength, sedimentation,thickening time, free water, cement mechanical properties (e.g., Young'smodulus, Poisson's ratio, specific heat, thermal conductivity, andpost-set expansion), wettability, emulsion, break time, pH, post-setpermeability, hydration time, post-set porosity, foam quality,permeability, expansion, water properties (e.g., pH, chlorides,bicarbonates, iron, tannin/lignins, carbonates, sulfates, magnesium, andcalcium concentration), and fluid break time (e.g., for fracturingfluids). Data may be collected using standard laboratory techniques orother suitable methodologies. By way of example, the rheology data maybe collected in accordance with the ANSI/API Recommended Practice 10B-2,Recommended Practice for Testing Well Cements, First Edition, July 2005.In some embodiments, historical data may be used so that additionallaboratory testing may not be required.

At step 14, the example method may further include developing a modelusing Barycentric interpolation that includes predicted rheology datafor a plurality of data points within the operational window of thefluid system. Density may also be determined for each of the data pointswithin the operational window. The Barycentric interpolation may use thecollected rheology data for the vertices of the sub-windows as the knowndata points in the interpolation. The interpolation technique may beadjusted to generate any number of data points within operationalwindow.

FIG. 3 is a block diagram of an exemplary computer system 15 that thatmay be used in performance of the techniques described herein. Softwarefor performing the interpolations and other method steps may be storedin the computer system and/or on external computer readable media. Thoseof ordinary skill in the art will appreciate that the computer system 15may comprise hardware elements including circuitry, software elementsincluding computer code stored on a machine-readable medium or acombination of both hardware and software elements. Additionally, theblocks shown are but one example of blocks that may be implemented. Aprocessor 16, such as a central processing unit or CPU, controls theoverall operation of the computer system 15. The processor 16 may beconnected to a memory controller 18, which may read data to and writedata from a system memory 20. The memory controller 18 may have memorythat includes a non-volatile memory region and a volatile memory region.The system memory 20 may be composed of a plurality of memory modules,as will be appreciated by one of ordinary skill in the art. In addition,the system memory 20 may include non-volatile and volatile portions. Asystem basic input-output system (BIOS) may be stored in a non-volatileportion of the system memory 20. The system BIOS may be adapted tocontrol a start-up or boot process and to control the low-leveloperation of the computer system 15.

As illustrated, the processor 16 may be connected to at least one systembus 22, for example, to allow communication between the processor 16 andother system devices. The system bus may operate under a standardprotocol such as a variation of the Peripheral Component Interconnect(PCI) bus or the like. In the exemplary embodiment shown in FIG. 3, thesystem bus 22 may connect the processor 16 to a hard disk drive 24, agraphics controller 26 and at least one input device 28. The hard diskdrive 24 may provide non-volatile storage to data that is used by thecomputer system 15. The graphics controller 26 may in turn be connectedto a display device 30, which provides an image to a user based onactivities performed by the computer system 15. The computer system 15may be programmed to perform operation and control methods of thepresent technique, including with regard to interpolation and comparisonsteps. The memory devices of the computer system 15, including thesystem memory 20 and the hard disk 24 may be tangible, machine-readablemedia that store computer-readable instructions to cause the processor16 to perform a method according to an embodiment of the presenttechniques.

To facilitate a better understanding of the present invention, thefollowing examples of certain aspects of some embodiments are given. Inno way should the following examples be read to limit, or define, theentire scope of the invention.

EXAMPLE 1

A model was developed to predict fluid rheology for a well spacer systemthat comprised water, a heavyweight additive, and a viscosifier. Theviscosifier used was SA-1015™ Suspending Agent, available fromHalliburton Energy Services, Inc. The heavyweight additive usedcomprises 50 weight % cement kiln dust and 50 weight % barite. Adispersant (CFR-3™ dispersant, Halliburton Energy Services, Inc.) wasalso included in an amount of 0.4% by weight of the heavyweightadditives. Depending on the source of the cement kiln dust, thedispersant may not be needed. The concentration of the dispersant can bevaried to minimize cost. The model was developed by determining anoperational window for the well spacer system, dividing the operationalwindow into four sub-windows and then conducting six baseline rheologytests at the vertex of each sub-window. Each baseline rheology testincluded the particular fluid recipe for each vertex tested at 80° F.,130° F., and 180° F. Barycentric interpolation was then used to predictrheology data for multiple data points (approximately 30,000) within theoperational window.

FIG. 4 is a graphical representation of the determined operationalwindow. The functional boundaries of the well spacer system were used todefine the operational window. The weight ratio of the heavyweightadditive to water (“HWR”) and the weight ratio of the viscosifier towater (“VWR”) were used as the boundary conditions. The operationalwindow was defined as follows: Vertex 1 (x₁, y₁), Vertex 2 (x₂, y₂), andVertex 3 (x₃, y₃), wherein x₁ is a HWR of 0, y₁ is maximum VWR, x₂ ismaximum HWR of 0, y₂ is minimum VWR, x₃ is a HWR of 0, and y₃ is minimumVWR. The maximum VWR was determined at an HWR of 0 by maximizing the VWRuntil an unmixable concentration of the viscosity and water is achieved.The maximum VWR was deteimined to be 0.0125. The minimum VWR wasdetermined by calculating the minimum amount of viscosifier required tosuspend the heavyweight additive at low shear rate. FIG. 6 is a chartrelating to material specific gravity and particle size that was createdto aid in determining minimum VWR. The minimum VWR was determined to be0.002. The maximum HWR was determined at minimum VWR by maximizing theHWR until an unmixable concentration of heavyweight additive in waterwas achieved. The maximum HWR was determined to be 1.565.

The operational window was then divided into four sub-windows, as shownon FIG. 5, represented as triangle α, triangle β, triangle γ, andtriangle ρ. Points 4, 5, and 6 on FIG. 5 were determined by calculatingthe midpoints between Vertices 1 and 2, Vertices 2 and 3, and Vertices 1and 3, respectively.

Baseline rheology tests were then conducted at the vertex of eachsub-window, i.e., Vertex 1, Vertex 2, Vertex 3, Point 4, Point 5, andPoint 6. Each baseline rheology test included the particular fluidrecipe for each vertex tested at 80° F., 130° F., and 180° F. Therheology tests were conducting in accordance with ANSI/API RecommendedPractice 10B-2, Recommended Practice for Testing Well Cements, FirstEdition, July 2005. The data for the six baseline rheology tests areprovided in the table below.

TABLE 1 Baseline Temp. Viscometer RPM Test (° F.) 300 200 100 60 30 6 3Vertex 1 80 80.5 78 74.5 70.5 66 53.95 50.25 130 73.5 73 69.5 66.5 62.551.8 48.6 180 65.5 64 61.5 60 56 48.2 45.75 Vertex 2 80 68.5 55 39.5 3225.5 16.7 14.8 130 64 51 38 31 26 17.9 16.7 180 72 58 43.5 36.5 31 26.7522.6 Vertex 3 80 11 9 8 7 7 6.6 6.45 130 10 8.5 8 8 7.5 6.95 6.55 180 109 8.5 8.5 8.5 7.9 7.45 Point 4 80 90 83.5 75.5 71 66 54.2 50.55 130 10093 84 79 73 61.3 58 180 90.5 86 78.5 73.5 69 61.35 59.85 Point 5 80 27.523 18 16.5 13 10.05 9 130 27 23 28 16 14 10.4 9.2 180 27 23 19 16.5 1410.7 10 Point 6 80 42.5 40.5 38.5 36.5 34 28 25.75 130 44.5 42.5 39.5 3835.5 28.95 27.1 180 46 45 42 40 37 32 30.4

After the data for the baseline rheology tests was collected,Barycentric interpolation was used to generate predicted rheologicaldata for a plurality of data points within the operational window.Approximately 30,000 data points were generated by the interpolation. AMicrosoft Excel spreadsheet was used to generate the predicted data. Inaddition to the predicted rheological data, the spreadsheet alsodetermined density of the fluid corresponding to each data point andspecific gravities of the materials used in the baseline rheology tests.

To more accurately predict a well spacer system ranging in density from8.35 pounds per gallon to 16 pounds per gallon, two additional modelswere developed. Model 2 and Model 3 further included varyingconcentrations of barite in the weighting agent. Below are the weightratios of cement kiln dust and barite that were used for each model:

Model 1-50 wt % cement kiln dust—50 wt % barite

Model 2-100 wt % cement kiln dust—0 wt % barite

Model 3-15 wt % cement kiln dust—85 wt % barite

EXAMPLE 2

Testing was conducted to evaluate the accuracy of the predictedrheological data generated using the models developed in Example 1. Aspacer fluid was selected using Model 3 (15% cement kiln dust—85%barite) having an HWR of 1.06 and a VWR of 0.0031. The selected spacerfluid corresponds to a data point in Model 3. The selected spacer fluidfrom Model 3 had a density of 14 pounds per gallon and composition ofthe spacer fluid was water (125.57 grams), cement kiln dust (22.50grams), barite (127.50 grams), viscosifier (0.43 grams) and dispersant(0.60 grams). The dispersant used was CFR-3™ cement friction reducer,available from Halliburton Energy Services, Inc. Rheology testing inaccordance with ANSUAPI Recommended Practice 10B-2, Recommended Practicefor Testing Well Cements, First Edition, July 2005, was conducted at 80°F., 130° F., and 180° F. to compare the actual rheological data with thepredicted rheological data from Model 3.

Table 2 below is a comparison of the predicted and actual rheologicaldata for the selected spacer fluid.

TABLE 2 Temp. Viscometer RPM (° F.) 300 200 100 60 30 6 3 Actual 80 5143 36 33 29 23 13 44 36 32 29 23 22 130 47 42 37 34 31 25 11 42 36 33 3025 23 180 48 43 38 36 33 28 23 43 38 35 32 27 25 Predicted 80 52 46 3733 29 22 20 130 50 45 38 34 30 25 23 180 49 44 37 34 31 25 23

Comparing the actual rheological data to the predicted rheological datafrom Model 3 shows very little variation, indicating that the modelaccurately predicted the rheological data for this particular datapoint.

EXAMPLE 3

Additional testing was conducted to evaluate the accuracy of thepredicted rheological data generated using the models developed inExample 1. A spacer fluid was selected using Model 3 (15% cement kilndust—85% barite) having an HWR of 1.06 and a VWR of 0.0031. The selectedspacer fluid corresponds to a data point in Model 3. The selected spacerfluid from Model 3 had a density of 13.5 pounds per gallon andcomposition of the spacer fluid was water (141.54 grams), cement kilndust (22.50 grams), barite (127.50 grams), viscosifier (0.43 grams) anddispersant (0.60 grams). The dispersant used was CFR-3™ cement frictionreducer, available from Halliburton Energy Services, Inc. Rheologytesting in accordance with ANSI/API Recommended Practice 10B-2,Recommended Practice for Testing Well Cements, First Edition, July 2005,was conducted at 80° F., 130° F., and 180° F. to compare the actualrheological data with the predicted rheological data from Model 3.

Table 3 below is a comparison of the predicted and actual rheologicaldata for the selected spacer fluid.

TABLE 3 Temp. Viscometer RPM (° F.) 300 200 100 60 30 6 3 Actual 80 4036 31 28 26 20 16 36 30 28 25 20 18 130 39 35 30 28 25 18 13 35 30 28 2520 18 180 38 34 30 28 26 21 19 35 30 28 26 21 19 Predicted 80 43 37 3027 24 18 17 130 41 36 31 28 25 20 19 180 40 36 31 28 25 20 19

Comparing the actual rheological data to the predicted rheological datafrom Model 3 shows very little variation, indicating that the modelaccurately predicted the rheological data for this particular datapoint.

It should be understood that the compositions and methods are describedin terms of “comprising,” “containing,” or “including” variouscomponents or steps, the compositions and methods can also “consistessentially of” or “consist of”0 the various components and steps.Moreover, the indefinite articles “a” or “an,” as used in the claims,are defined herein to mean one or more than one of the element that itintroduces.

For the sake of brevity, only certain ranges are explicitly disclosedherein. However, ranges from any lower limit may be combined with anyupper limit to recite a range not explicitly recited, as well as, rangesfrom any lower limit may be combined with any other lower limit torecite a range not explicitly recited, in the same way, ranges from anyupper limit may be combined with any other upper limit to recite a rangenot explicitly recited. Additionally, whenever a numerical range with alower limit and an upper limit is disclosed, any number and any includedrange falling within the range are specifically disclosed. Inparticular, every range of values (of the form, “from about a to aboutb,” or, equivalently, “from approximately a to b,” or, equivalently,“from approximately a-b”) disclosed herein is to be understood to setforth every number and range encompassed within the broader range ofvalues even if not explicitly recited. Thus, every point or individualvalue may serve as its own lower or upper limit combined with any otherpoint or individual value or any other lower or upper limit, to recite arange not explicitly recited.

Therefore, the present invention is well adapted to attain the ends andadvantages mentioned as well as those that are inherent therein. Theparticular embodiments disclosed above are illustrative only, as thepresent invention may be modified and practiced in different butequivalent manners apparent to those skilled in the art having thebenefit of the teachings herein. Although individual embodiments arediscussed, the invention covers all combinations of all thoseembodiments. Furthermore, no limitations are intended to the details ofconstruction or design herein shown, other than as described in theclaims below. Also, the terms in the claims have their plain, ordinarymeaning unless otherwise explicitly and clearly defined by the patentee.It is therefore evident that the particular illustrative embodimentsdisclosed above may be altered or modified and all such variations areconsidered within the scope and spirit of the present invention. Ifthere is any conflict in the usages of a word or term in thisspecification and one or more patent(s) or other documents that may beincorporated herein by reference, the definitions that are consistentwith this specification should be adopted.

What is claimed is: 1-11. (canceled)
 12. A method of servicing a wellbore comprising: providing an optimized cement composition, wherein theoptimized cement composition is based, at least in part, on a modeldeveloped using Barycentric interpolation; and introducing the cementcomposition into a well bore.
 13. (canceled)
 14. The method of claim 12,further comprising determining an operational window for a well borefluid system; collecting data at vertices of the operational window; anddeveloping the model comprising predicted properties for a plurality ofdata points within the operational window, wherein developing the modeluses Barycentric interpolation.
 15. The method of claim 14, wherein thetwo or more boundary conditions comprise mass ratio of weightingadditive to water and mass ratio of viscosifier to water.
 16. The methodof claim 14, wherein the operational window comprises a triangular,two-dimensional window.
 17. The method of claim 14, wherein theoperational window is defined as follows: Vertex 1 (x₁, y₁), Vertex 2(x₂, y₂), and Vertex 3 (x₃, y₃), wherein x is a first boundary conditionfor the well bore fluid system and y is a second boundary condition forthe well bore fluid system. 18.-20. (canceled)
 21. The method of claim12, wherein data from the well bore, comprising data points, is sent toa processor that is coupled to memory, wherein the processor isconfigured to receive the data from the well bore and develop the modelusing Barycentric interpolation, the model comprising predictedproperties for a plurality of data points within an operational windowof the treatment fluid.
 22. The system of claim 21, wherein theoperational window comprises two or more boundary conditions for thecement composition fluid.
 23. A method of servicing a well borecomprising: determining an operational window for a well bore cementcomposition system, wherein three or more vertices are selected thatdefine boundary conditions for the well bore cement composition system;dividing the operational window into sub-windows; conducting a lab testto collect data at the three or more vertices of the operational window;and developing a model with a computer system, wherein the model isbased at least in part on the data, wherein the model comprisespredicted properties for a plurality of data points within theoperational window, wherein developing the model uses Barycentricinterpolation; providing an optimized cement composition, wherein theoptimized cement composition is based, at least in part, on the modeldeveloped using Barycentric interpolation, and wherein the optimizedcement composition is optimized based on rheology; preparing theoptimized cement composition; and introducing the optimized cementcomposition into a well bore.
 24. The method of claim 23, wherein thetwo or more boundary conditions comprise mass ratio of weightingadditive to water and mass ratio of viscosifier to water.
 25. The methodof claim 23, wherein the operational window comprises a triangular,two-dimensional window.
 26. The method of claim 23, wherein theoperational window is defined as follows: Vertex 1 (x₁, y₁), Vertex 2(x₂, y₂), and Vertex 3 (x₃, y₃), wherein x is a first boundary conditionfor the well bore fluid system and y is a second boundary condition forthe well bore cement composition system.
 27. The method of claim 23,wherein data from the well bore, comprising data points, is sent to aprocessor that is coupled to memory, wherein the processor is configuredto receive the data from the well bore and develop the model usingBarycentric interpolation, the model comprising predicted properties fora plurality of data points within an operational window of the treatmentfluid.
 28. The method of claim 23, wherein the operational windowcomprises two or more boundary conditions for the cement composition.29. A method of servicing a well bore comprising: providing an optimizedcement composition, wherein the optimized cement composition is based,at least in part, on a model developed using Barycentric interpolation,and wherein the optimized cement composition is optimized based onrheology; preparing the optimized cement composition; and introducingthe optimized cement composition into a well bore; wherein the model isbased at least in part on data collected at three or more vertices of anoperational window defined by boundary conditions for the optimizedcement composition, wherein the model comprises predicted properties fora plurality of data points within the operational window.
 30. The methodof claim 29, wherein the two or more boundary conditions comprise massratio of weighting additive to water and mass ratio of viscosifier towater.
 31. The method of claim 29, wherein the operational windowcomprises a triangular, two-dimensional window.
 32. The method of claim29, wherein the operational window is defined as follows: Vertex 1 (x₁,y₁), Vertex 2 (x₂, y₂), and Vertex 3 (x₃, y₃), wherein x is a firstboundary condition for the optimized spacer fluid composition and y is asecond boundary condition for the optimized cement composition.